We would have no success if we tried to define mensuration in a few words by picking up some elements of our modern notation system. On the contrary, we'll set up its main rules by pointing out some modern features which did not exist formerly:

This is striking at first sight, and it will remain a problem as long as we won't become familiar with the very heart of this music: we'll have to listen to sentences paced by the tactus, instead of counting values fitting a regular time signature.
But let's be realistic: though we all wish to discover this music, we're not necessarly wishing to enter a long range learning curve (AFAIK I'm just walking my first steps). And, even if it would be the case, an immediate listening would be a useful motivation...
After all, why should we transcribe to modern notation? As a matter of fact, I currently have no other mean to create sound files, since the Encore score editor that I'm using only knows about measured notation. Not to mention the pleasure to meet and play this music, taking in account goodwills and scores available to us, amateurs...

However, if you're interested in practicing this beautiful early notation, here is a learning program suggested by Sybrand Bakker, who has got a great experience in singing and playing it :

don't try to transcribe, forget about modern notation ; and get used to the various C clefs;

begin with the white mensural notation used in the 1500s (that's what we're doing here), simpler than the former black one (however, let me add - hoping Sybrand won't mind: I remember having read a different opinion on this point in the newsgroup rec.music.early!) ;

then one could practice the Chansonnier for Marguerite of Austria (Brussels 228, available from Alamire), containing for example a triple canon for six voices, Ave Sanctissima Maria, perhaps written by Pierre de La Rue;

then, you could read the Burgundian Choirbook (Brussels 5557, also available from Alamire), containing the mass Ave Regina coelorum by Guillaume Dufay ;

then only, try to gradually move to older music.

While writing these pages, I realized that I had no exact idea about the reason for barlines in modern notation! Thus, I once asked about that in newsgroups, and most persons seem to think that it's more a tool making easier to work on music, rather than an essential element of its expression:

First, barlines don't help to read a piece in which musical ideas have various rythms and lengths, and, conversely, when reading a dance, one may think that barlines aren't indeed saying anything more than the music itself.

But not everybody agrees on this point: Sybrand Bakker, already mentionned, thinks that barlines do bring structural information in dances published at the end of the 1600s.
I haven't had a chance to submit him a few objections: first, it seems that this kind of dances appeared somewhat before these years; secondly, one has often to make a decision inside a measure - just think about hemioles occurring so often; and, last, strangely enough, I remember having read in Apel about pieces from the beginning of the 1600s, published later on in this century, with barlines added in a very weird way!

By the way, it's interesting to notice that barlines appeared around 1600, at the moment when music began to be published in vertical scores like it's the case nowadays. Formerly, pieces published for performance were layed out in separate parts, that is, one part after the other (the whole cantus part, then altus, etc): have a look at the facsimiles shown on this site. Meanwhile, for their personal usage, composers sometimes wrote their music in vertical scores, and this is quite understandable!

First, when a note must go across a barline; thus we won't come upon such a situation, and that's a good point, since this notation artefact leads sometimes to write identical rhythmic patterns in different ways!

Then, a tie is sometimes used to make reading easier, or to suggest some accent in time signatures involving dotted values.

Last but not least, some values must be written with ties, by adding smaller values. And here we come to the very heart of our subject: since ties didn't exist in the renaissance, mensuration system wrote composite values in a different way.

Nowadays all value ratios are binary: a whole note is equal to two half notes, each of them being equal to two quarter notes, and so on. Formerly some ratios were ternary, and this is more and more true when looking at older music, because these ternary ratios - which were said perfect - were the very foundation of the system. We use to think today, and there's some evidence for that, that this idea of perfection was first related to the ternary nature of God.

Mensuration signs found at the beginning of each part told which notes were in ternary or in binary relationships. Mensurations weren't necessarly the same in each part, and they might change when a new sign was written further inside the staff.

That's probably the most astounding feature of the system at first sight, but also the most specific and the most understandable one, if we remember the lack of ties. Since new values couldn't be built by adding smaller ones with ties, they were obtained by substraction: in a ternary mensuration, a long note may be made shorter by some smaller note standing on its right or left side!

Though the mensuration sign first specifies that a perfect note weights three smaller ones, this long note may be imperfected by a neighbouring smaller note, and then weights only two of them; the total values still amount to three, and this is called a perfection.

These basic principles will be better understood when we will have said enough to be able to give examples..

At first sight there's no tempo indication for any music of this time, but that's not true, because it was indeed included in mensuration signs, at least when considering their standard meaning at the very beginning of the system: several documents of this time show singers touching each other's shoulders with hands, in order to beat the tactus, which specifies that a semibreve (our whole note) should be played roughly as fast as human heart beat.

This definition shouldn't be taken too strictly (we know that a performance might change according to the room size or other circumstances), but it's nevertheless an indication of tempo, for this is proven by the existence of proportion signs which specified that the music had to be sometimes played twice, third, ... as fast or as slow. Proportion signs are an extremely complex subject, because they were written with many different symbols, about the meaning of which theoreticians were fighting each other! For instance, the meaning of the symbol still in use today has changed in a rather obscure way, which hasn't been fully understood up to now, though it might have looked so simple at first sight... (this point is mentionned in a few words in Apel page 192, and widely investigated in Busse Berger).

That's why we will study only basic mensuration signs: those specifying a performance according to the unitary tactus (integer valor), that is, at the approximative tempo of a semibreve per human heart beat. To avoid any misunderstanding, let's add that a tactus or battuta is made of a downbeat and an upbeat on every semibreve.

It's obvious indeed: how could we have several downbeats without any upbeat in between?

We will start from a facsimile like those available on the site, and we'll get its transcription into modern notation, and then we'll even be able to listen to it: if you haven't did it yet, please go and listen to my transcriptions of Josquin, Barbireau, Mouton, etc, on the page dedicated to pieces from the renaissance, I guess this will give you some reason to read the following lines!

Of what steps will be this process made of?

First be careful to chose an easily readable facsimile. It's more important than you might think at first sight, since my experience has been that the bad condition of a document may lead to more problems than the transcription rules themselves: some continuation signs may refer to various places on the sheet, some notes have been emendated, some note stems are hardly visible, some rests
may look like points - or conversely - all these problems can be real traps for the beginner that we still are at the present time!

Then, you'll have to change ligatures on the manuscrit into separate note symbols, like those we write today. I think this is a simple and pleasant process, which is explained on my page about ligatures. Having done so, you'll get a sequence of notes, but you won't know yet their value ratios, which are specified by mensuration, our present subject.

Thus, the last step will be to read the mensuration signs, in order to know the transcription rules toward modern notation. I'd advise you to begin with a piece written in binary mensuration, that you'll read quite easily: it's a good idea to practice each new point after the other, rather than trying to deal with all of them simultaniously.

I won't give once more the note names shown at the beginning of the page about ligatures; instead I'll give only their abbreviations and symbols, with a new line dedicated to rest symbols:

Mx

L

B

S

M

Sm

F

Sf

or

or

or

or

Beware, rest values, like note ones, depend on mensuration. For instance, when a breve is equal to three semibreves, the same is true for the corresponding rests...

One can see that our modern rests nearly look like former ones, with a striking exception: today a whole note rest is said to hold for the whole measure - whatever the time signature might be, while other rests have all the same duration as the corresponding note.

The various symbols for maxima and longua rests will be explained later on.

Now, a few words about a practice quite usual amongst many editors: dividing note values. If you don't, it means that you'll transcribe a semiminim by a quarter note, a minim by a half note, then, according to mensuration, a semibreve by a dotted or undotted whole note, a breve by a dotted or undotted square note, a longua by two or three tied square notes, and a maxima, which is nearly always binary, by four tied square notes!

Shall we preserve this 1:1 ratio in the transcription?

I'd answer yes, every time we don't get a cumbersome modern transcription, that is, in all cases but those which involve a part written in very long values from its beginning to its end, like would be the case of a cantus firmus, for instance. In this latter case, and only then, we'll have to divide all values by four, for instance, and thus transcribe maximas by square notes, ternary or binary longuas by dotted or undotted whole notes, etc, and semiminims by semiquavers.

In every other circumstance I by far prefer not to divide values, for both aesthetic and reading reasons: I can't see any problem with time signatures like 2/1, 3/1, 6/2, etc, that some editors have been using more and more often when publishing canzonas, for instance; furthermore, as an amateur, I'm often playing with hystery when only speed is required, and thus reading quarter notes instead of semiquavers in diminutions helps me to play them in a cooler way...

That's a pleasant example of getting something positive from a cultural gap: obviously, any renaissance amateur having the same problem as mine would have been frightened by semiminims like I'm by semiquavers!

Whenever you have good reasons to divide values, you'd rather get first an undivided version which will be more easily compared with the original if necessary. Failing to do so in my first attempts, I had several times to erase many lines which I had translated so painfully! Don't forget that you're working on parts without vertical "milestones": applying simultaniously translation rules for ligatures, mensuration rules - some of them rather tricky, and division ratios on note symbols quite new to us, that's perhaps a little too much to begin with...

I'm happy to give you now good news, rather than bad ones: indeed, only two levels of division are really relevant in most cases, and they are: how many semibreves (whole notes) in a breve (square note), and how many minims (half notes) in a semibreve.

At lower levels, the ratio is always binary, like it is nowadays: a minim is equal to two semiminims (quarter notes), a semiminim to two fusas (quavers), and a fusa to two semifusas (semiquavers).

Higher levels, maxima => longuas => breves, are not so often relevant: they're binary in the absence of a different indication, and thus we'll tell about them later on.

Division of breves into semibreves is called tempus. When ternary, this division is called tempus perfectum, when binary it is called tempus imperfectum.
Ternary division of semibreves to minims is called prolatio major, and binary division is called prolatio minor.

Don't get confused because of these different names: major and minor are indeed the perfect and imperfect instances of the division prolatio.

In real musical life, we'll always need to specify the nature of both levels of division, thus we'll have to deal with four possible combinations: perfect time - major prolation, perfect time - minor prolation, imperfect time - major prolation, and imperfect time - minor prolation. Besides that, the history of the system and the design of mensuration signs would suggest to study first the perfect ternary mensurations.

However, I've choosen a different way to tell you this story, which I hope to be simpler just because the learning curve will be smoother:

first we'll study the binary division, because it's by far the simpler one, beeing quite close to our modern notation;

then we'll study the rules for a single ternary division, which might as well be time or prolation, since their rules are quite similar;

and then only, we'll look whether this similarity remains true in every detail, and whether dealing with two levels of division at the same time leads to remarkable interactions.

Now it's time to give the mensuration rules, that you'll find on the next page.

In case you'd wish to go deeper in this subject, or to compare my contribution with the sources that I've used to write it, you might have a look at the bibliography. But remember what I told you a few moments ago about proportions: don't read about them without some aspirin quite ready, oh... we might say willow leaves, to set up a more renaissance mood :-)